I have been in this situation before.  You may have a separate business entity for the A/E firm.  Simply bill the "client" as you would any other customer.  Are jobs done on a T/M basis, or fixed fee?  If fixed fee, you can use hours saved as a bonus method for the employees.

We have recently started to bill the client as we would any other.  The dificult thing has been to get everyone to slow down and actually do cost estimates.  When you work in the same office as the clients, the projects move at lightening pace.  The clients drop new projects on your desk and want work to begin immediately.  When this happens we bill T&M.  If I can get everyone to slow down for a couple of days I get some solid numbers together and work fixed-fee.  Some of the civil projects have gotten out of hand with regard to fees.  No scope. No fee schedule. Just design it.  Changes happen daily and the fees creep to crazy levels.  It is great to not have to chase down work month to month but being "in-house" has its challenges.

I have been in that exact situation.  I worked with an "in-house" engineering company for a contractor.  We had a lot of "just get it done!" work, but we would always put a number to it.  The number may be provided a week or so after we started the project, but it would almost always get a fixed fee number.  It can be very challenging in those situations.