A 135 job should pay more than a regional job because corporate/charter flying and the airlines are NIGHT AND DAY different. People who charter a multi-million dollar aircraft aren't looking for the cheapest ticket on Priceline - they are looking for privacy and convenience and superior service... and as a pilot you deserve to be properly compensated for providing that.
IMO minimum pay for a BE400A SIC in the Midwest should be 30k + benefits. MINIMUM. Chicago = a little bit more than that. You should not subsidize a scumbag operator by allowing them to 1. pay you jack to fly a multi-million dollar turbine aircraft around, 2. cheaply do all your training in-house instead of formal training, and 3. have no QOL with only 5 hard days off. Yeah you'd be making similar money to GUARANTEE at a regional...but no perdiem, no ability for overtime/opentime, and half the hard days off of even the worst bottomfeeder.
I turned down a Beechjet SIC job around Chicago a little over a year ago because the guy wouldn't discuss pay. I was current on the airplane and he 'needed me yesterday', but wasn't willing to talk dollars and cents. No thanks...