I have about 6 months left on contract and I would like to purchase a home but they require proof of employment. Will they see that I won’t be in the military for long?

I really want to purchase my first home. I have never made a late payment on my debt, I have $6k consolidated debt. A credit score of 713. My husband and I recently got married and he’s got 645 credit score, late payments and $30k in debt. He would have stable income but with his poor credit and payment history, I wonder if it would be better to put the house only in my name. I could use any advice!