What is the basis for buying out my husband's share of our house for a divorce?

I do not understand your question. Buying out his interest in the house is a financial issue, although there could be emotional ties to it as well. If you have children and they are mostly staying with you, Florida law presumes that it is in the children's best interest for them to continue living in the house. maybe you can use that argument.

The basis is called equitable distribution. We start out with a 50/50 division of the assets and marital obligations and come up with a plan that will be agreeable to both parties.