I sold a home solely in my name in 2016. My husband may sell his home in 2017. If we file married but separately, will we both avoid paying capital gains?

It depends.  Filing Married Filing Separately, each of you would be allowed to exclude up to $250,000 of gain on each sale of the home if it qualifies for the exclusion for sale of a prinicipal residence.  The following FAQ provides more information on the exclusion:  https://ttlc.intuit.com/replies/3300213.

This may end up being the better way to handle the sales of the homes in your case.  Although filing joint you may exclude 500,000 per home sale, but it seems like you have to wait two years before you can sell the second home, and it must also constitute a principal residence.  This IRS website gives a good deal of information on the rule, but does not address MFJ filings for your situation.  Nevertheless, it is the strongest authority on this subject:  https://www.irs.gov/uac/irs-issues-home-sale-exclusion-rules

Just be aware that Married Filing Separately, while probably recommended for your situation, carries potential complications, especially if you are in a community property state.  Again, this FAQ can give guidance to assist you if this is your situation:  https://ttlc.intuit.com/replies/3301943