Your situation qualifies for the exception to the rule that a married couple must file as either Married Filing separately (MFS) or Married Filing Jointly (MFJ). If you lived apart from your spouse the entire last half of the year and you each have a qualifying child, you may each file as Head of household.
The rule about a spouse not being able to use the standard deduction if the other spouse itemizes only applies to those using MFS status. So, you can each use standard or itemized, as fits your needs.
