Montgomery County Executive Charles Gilchrist yesterday proposed a $664.8 million budget for next year that would cost the owner of an average county home an additional $16 in property taxes.

The proposed 1980 budget, up more than 8 percent from this year, would provide substantial funding increases for transportation and housing, and a modest increase for education, which has left public school administrators unsatisfied.

Most members of the County Council, which must set the final budget and tax rate by May 15, called Gilchrist's proposal prudent. Council members said they probably would not cut the budget, but might have to add to it, particularly if the county gets less money than anticipated from the state government.

Since one-third of the homes in the county are being reassessed this year, the new property tax rate will not apply equally to homeowners. The $16 tax increase would apply to average $80,000 homes that have not been reassessed. The owner of an identical home that has been reassessed would pay an additional $150 in property taxes.

One-third of the homes in Montgomery are reassessed every year. Property in the county is assessed at 50 percent of market value. The proposed budget would raise the tax rate from $3.30 to $3.34 per $100 of assessed valuation.

Gilchrist allocated more than 40 percent of his proposed budget, $307.7 million, for schools. The school board requested $314 million, and School Superintendent Edward Andrews said he was disappointed at Gilchrist's proposed budget.

"My impression is that he's tried to be fair, but that's not enough to pay our teachers their negotiated 10 percent salary increases and also keep our educational programs intact," Andrews said.

Gilchrist said that he supports the 10 percent salary increase for teachers, and that the school system should trim its budget in other ways. "While there are those who think it's too great a cut, we think not," Gilchrist said. "The county government itself will increase less than that."

The county government buget would increase by 5.8 percent over the current year's budget, while the school budget would rise 8.4 percent.

Council President Scott Fosler said the council is committed to keeping the 10 percent salary raise for teachers in the budget and that the council may decide to give the Schools more money than Gilchrist proposed.

Gilchrist said his budget reflects his priorities of expanding the public transportation system to conserve gasoline, expanding the housing supply and providing adequate police and fire protection.

Under the executive's proposal, the mass transit system budget would be increased the greatest percentage of any item, to $31 million, up 25.5 percent over last year's budget.

The increase would be used to finance the operation of 42 new buses and a 23 percent increase in bus hours for the county's Ride On minibus service. About 50 new employes, most of them drivers, would be hired for the expanded bus system.

Fosler said Gilchrist's budget "makes sense," but that the council may have to increase the property tax rate more than Gilchrist proposes. "The budget assumes that we'll get $10.5 million in aid from the state," Fosler said. "If the state doesn't come through, it could mean that we have to increase taxes."

Fosler said it is likely that the state will give the county $8 million of the expected $10.5 million in mass transit and highway use revenue, but that it is unclear whether the county will get the rest of the money for education and police aid.

The funding for county government operations, the second largest item in the budget at $107.3 million, would increase the lowest percentage of any item compared to last year's budget.

Gilchrist has recommended eliminating about 100 county positions, although 50 new ones would be gained when the Ride On bus service hires its drivers. Most of the positions would be eliminated through attrition: about a dozen would be eliminated through transfers and layoffs. Gilchrist said he is not imposing a hiring freeze.

Gilchrist also allocated $2 million for loans for tenants with limited income who want to place down payments on the apartments when they are converted to condominiums; and he recommended that the county hire five additional persons to help people with rental and condominium conversion problems.