If the majority party in the house is the democratic party, then the minority is

Republican party.

Explanation:

In the history of United States of America the two main parties that has been ruling for a long time now are the democratic party and the Republican Party although there are some minor parties that are not stable such as Green Party of the United States of America and so on.

Just from the question, it shows that a large number of people holding public office in the house are that of Democratic party which confers the 'majority' title to the party and the party with the lesser number of people holding public office in the house are that of Republican party and that makes them the 'minority' party