"Husband, father, president -- he's done these three jobs with distinction." --Announcer in one of President Carter's campaign commercials.

In his private study, tucked away behind the formal Oval Office, President Carter was taking time from his crises to cut a tape for a television commercial.

There was no script. Just what the president's advisers would later call "free discussion."

But out of that unscripted session grew a subtle theme that fit right in with the master script of President Carter's plan for defeating Sen. Edward M. Kennedy's (D-Mass.) challenge for the presidential nomination.

Months ago, the president's top campaign strategists concluded that Kennedy -- and the way Kennedy would conduct his presidency -- would have to be made to be the issue of the 1980 campaign.

Carter's pollster, Patrick Caddell, had concluded that the public viewed Carter's character as his greatest strength and that there was significant doubt about Kennedy's character, according to senior Carter advisers.

Now the Carter people have devised a series of television campaign commercials, just beginning to air in Iowa, which draw that distinction between Carter and his opponent in subtle undertones, never mentioning Kennedy.

The ads end with a carefully constructed solgan about Carter: "A solid man in a sensitive job." These are ads about Carter and farm policy, Carter and tax policy, Carter and national defense. But there is another Carter ad that is about none of these issues, but which brings home the unspoken contrast between Carter and his chief opponent.

It features scenes of the president helping his daugther, Amy, with some vexing new math homework, and of the president with his wife, Rosalynn. the words that accompany these scenes are Carter's own, spoken by his and born in that session in his study.

In that room, TV producer Robert Squier and Carter's media adviser, Gerald Rafshoon, had told the president they had some taped footage of his family, and they asked him to talk about them.

"I don't think there's any way you can separate responsibilities of being a husband or a father and a basic human being from that of being a good president," Carter said. "What I do in the White House is to maintain a good family life, which I consider to be crucial to being a good president."

The microphones caught Carter's words, the tape recorder preserved them, and they became part of a half-hour commercial that the Carter-Mondale campaign aired nationally last Sunday over the ABC network. From that, a quick 30-second TV commercial was cut for use in Iowa.

The ad opens with an announcer's voice: "The White House is today the pivot point of some of the most important decisions in the world. It is also a home." Then comes the footage of the Carter family and Carter's comments. aAnd all of this concludes with an announcer's pointed observation: "Husband, father, president -- he's done these three jobs with distinction."

Carter's family message affords a sharp but quiet comparison with Kennedy, who has had marital problems with his wife, Joan, and has lived separately from her for some time (although she has been making some campaign appearances alongside him.)

The Carter advisers are understandably reluctant to discuss the intent of their Carter family commercial. "I suppose you could say it is a sharper contrast" to California Gov. Edmund G. (Jerry) Brown Jr., who is unmarried but friendly with singing star Linda Ronstadt, said Squier, when asked if he had intended a comparison with Kennedy in his ad. "The film speaks for itself," Rafshoon said "The point is, when you have a family, you play it up. I mean, what politician doesn't play up his family?" He added, "It isn't negative advertising, it's positive."

Rafshoon has made use of another theme -- telling the truth -- which the Carter advisers say was intended to draw a distinction with Kennedy. Polls have shown that large numbers of Americans do not believe Kennedy's explanations of the Chappaquiddick incident.

The truth ad shows Carter answering questions on various questions in his town meetings, and conclude with the announcer saying:

"You may not always agree with President Carter.But you'll never find yourself wondering if he's telling you the truth. It's hard to think of a more useful quality in any person who becomes president than telling the simple truth."

Rafshoon concedes that this spot is intended as a swipe at Kennedy. "Look, we wouldn't be using the truth spots as much if Teddy wasn't demagoguing and not telling the truth in his campaign," he said. But, he added,"It also can be seen as being about some of the other candidates too."

The Carter ads will have to serve in Iowa in place of personal campaigning, which both Kennedy and Brown are doing in an effort to win support in the Jan. 21 presidential caucuses. This personal campaigning is the sort of thing the president's advisers have always felt is Carter's strong suit. Now they have constructed an ad they hope will be the next best thing: Carter chatting with an Iowa farmer in the Oval Office.

"Well, nothing's more important to me than being with you," Carter tells the farmer. "My wife and I were talking today at lunch about your being up here."

The farmer: "I had a nice little visit with her this morning."

Another ad -- perhaps the most powerful of the Carter collection for 1980 consists solely of an Oklahoma mother of three sons standing up at a town meeting and, choking back tears, thanking Carter for his "role as a peacemaker today." The audience stands and applauds, and it is this applause that fills the remainder of the 60-second spot.