Our assets are equal if he keeps his $90,000 pension and she keeps the $80,000 house. Are we required to divide?

The answer to your question is no; within $10,000 you have basically equally divided the estate. Technically, $5,000 is owed. However trading lucrative pension benefits for keeping the house is not always a good financial move. Make sure the pension is professionally valued so you know what is really currently worth; also consider what receiving 50% of your spouse's monthly pension at retirement over your life time means to you, so you can make an informed decision whether keeping the house and being one hundred percent responsible for its upkeep and maintenance , is really in your best financial interest. Consider talking to a family lawyer or financial advisor about this, before making a final decision.