Have you seen this ? The term "flow through" can be misleading with details in the fine print.
My understanding of Part 121.436 is that for a pilot to enter to a captain position, he must have 1000 hours of
FAA Part 121 (Part 121 SIC fills that requirement)
time so it doesn't appear your husband's EASA TPIC would satisfy that requirement. People who know more than I can correct my impression as necessary:
https://www.hawaiianairlines.com/careers/first-officer
https://www.cbizems.com/extranet/JobSearch.aspx?id=128861&aid=17088
http://www.empireairlines.com/careers/ohana/
https://www.law.cornell.edu/cfr/text/14/121.436