The 241,000 customers of the Washington Suburban Sanitary Commission in Washington's Maryland suburbs can expect to pay an average of 10.8 percent more for water and sewer service, starting in July.

An average family would find its combined annual bill rising from about $185 to $205 under higher water and sewer rates, which the commission said yesterday whould be necessary under its preliminary budget for the fiscal year beginning July 1.

The $358,956,800 preliminary budget, approved unanimously by the six commissioners, would require a 6 percent increase in the water rate and a 15 percent increase in the water rate and a 15 percent increase in the sewer rate.

The WSSC provides water and sewer service to Montgomery and Prince George's counties.

Under President Carter's anti-inflation price guildelines, the WSSC would, in general, be limited to a 9 1/2 percent increase in its rates. Although the sewer rate would be increased 15 percent that increase would not violate the guidelines, a WSSC spokesman said, because of an exemption covering new facilities and equipment.

Most of the sewer rate increase, the spokesman said. would be used to cover costs of expanding and upgrading the Piscataway and Western Branch plants in Prince George's County and acquiring new sewage sludge compsoting sites in Prince George's and Montgomery counties.

The Piscataway plant is being expanded from a capacity of 18 million gallons daily to 30 million gallons-or enough to serve about 300,000 people. The Western Branch plant is being expanded from 15 million gallons daily to 30 million gallons, too. Both are also begin upgraded to more expensive advanced treatment of sewage.

Underuse of the plants, because they were built to handle more growth than now is expected in Prince George's, will cost the WSSC millions of dollars annually in lost revenues, the agency estimated last year. A considerable portion of the lost revenues could be recaptured, Montgomery officials have maintained, if Prince George's would share its capacity with its neighbor, which has to send most of its sewage to the Blue Plans regional plant in the District of Columbia.

While Prince George's officials have in the past generally resisted sharing, WSSC chairman Johanna Norris, who represents the county, said yesterday: "We're going to have to utilize some of that excess capacity. Prince George's will be reasonable-we'll have to be reasonable."

She said she supports proposals by the District and - more recently-by Prince George's County Executive Lawrence J. Hogan and the County Council for a regional conference on sharing. While Prince George's has a sizable surplus, both the District and Montgomery are running short. To avoid a possible swer moratorium in 1980, the District recently said it was taking an extra 5 million gallons daily at Blue Plains-an action denounced as illegal by suburban Maryland.

The WSSC's preliminary budget, drawn up by the Budget and Fiscal Review Committee, is about $6.9 million more than the current one of $352,027,000. Construction would decrease about $10.7 million-to $220,441,800-but operating expenses would go up almost $17.7 million-to $138,545,000.

The budget would put a 6 percent ceiling on cost-of-living salary raises, and would permit no raises-including merit raises to exceed 7 percent,

"This is one of the tightest budgets I have seen," said Norris, an eight-year veteran of the bicounty agency, which serves 1.2 million people in the two Maryland counties.

The detailed budget will go to public hearings in February. It will have to be approved by the two county councils as well as the WSSC commissioners.