Can I qualify for a mortgage loan?

My husband and I are wanting to buy a home (after many years of renting). We have a good monthly gross income ($11,500). However, we have a lot of credit card debt (61K) and a small balance on a student loan(6.5K). Our auto loan is payed in full and we have never had any late payments on any of our debts. Our credit scores are about 750 each. We lived in the same home for 6 years and have had stable employment for 17-18 years. Will a lender give us a mortgage with this level of unsecured debt?