My husband and I are in the process of divorcing and have two children. Can each of us file as married filing separately and each claim one child as a dependent?

Yes, you can file as married filing separately and each claim one child as a dependent.

However, each of you may be able to claim Head of Household, (entitling you to a larger standard deduction and possibly lower tax rates), even if you were legally married as of December 31. 

You are considered unmarried (and therefore eligible for Head of Household) if all 5 of these conditions apply:

1. You won't be filing jointly with your spouse; and
2. Your spouse didn't live in your home after June (temporary absences due to illness, school, vacation, business, or military service don't count); and
3. Your home was your child's, stepchild's, or foster child's main home for more than half the year (non-child dependents in your home don't qualify); and
4. You paid more than half the costs of keeping up your home during the tax year; and
5. You meet the qualifications to claim the child as your dependent, even if the other (noncustodial) parent is actually claiming the child as a dependent on their return.