Paul:
The approach appears to be logical since there is nothing in the Code for this exact condition.
Make sure the bottom of the steel columns is pinned, so, you don't have to check the compatibility or relative rigidity between the two. Good luck with the Building & Safety!
Farzin S. Rahbar, SE
David C. Weiss Structural Engineer & Associates, Inc.
(818) 227-8040 Ex. 13 Fax: (818) 227-8041
David C. Weiss Structural Engineer & Associates, Inc.
(818) 227-8040 Ex. 13 Fax: (818) 227-8041