Consider carefully if you want to keep the house right now. I mean, if you can easily afford it, fine. Bur of not, consider the following scenario:

(Numbers just for the sake of demonstration)

House worth $300k (let's assume it's paid off for the sake of our example)

Scenario 1: You pay ex $150 k to buy him out

Market stays flat
You decide to move in a couple of years (for a job or new relationship or retirement)
You sell the house for $300k
You pay 6% closing costs, $2k in fixing the house up for sale, and get $282k from the sale of the house. You also have to pay capital gains on $32k of that money. So H got $150k from the house and you only get about $129 k.

Scenario 2:
Market falls and in a couple of years house is only worth $200k

You decide to move (for a job or new relationship or retirement)

You sell the house and pay the 6% seller's costs and $2,000 in repairs to get it ready to sell, so you realize $180k. So basically, your H got $150k from the house, and you only realized $30k from the house.

This is the danger of holding on to your house in a falling market if you are not SURE you can and want to stay in the house for many years.

Another worse scenario is if you hold onto the house but cannot afford it and end up losing it to foreclosure - then you paid H $150k and end up with nothing (hopefully that would not be an issue for you).

The question is - would you buy your house today for what it appraises for today? Does that fit into your post-divorce budget? Could you keep it even if he welches on alimony? Can you afford any major repairs that might come up (new sewer line, new roof, new furnace, things like that?) If the answer is no, then you may want to sell the house. If you could afford it at current appraisal without his help and do want to keep it longer term, then get the appraisal soon and buy him out before interest rates go higher.