If you plan to buy a house in half a year, and you do need to buy a new car, buy it now. After paying car loan on time for 6 months, your credit score will be same or even better.

The potential problem is not credit score, but the DTI ratio (debt to income). When you apply for mortgage, the DTI ratio will determine how much money you car borrow. If your income is high enough, the monthly car-loan payment may not matter that much though.

In addition, yes, your husband can apply for car loan himself, and you can apply for mortgage as the sole borrower. They will check the credit score of mortgage borrower(s).