My docs (past 2 sub docs) have had no issues prescribing both meds to me, except I now get subutex instead of suboxone, 8mg a day.. and 3mg of kpin a day with a few extras... My current doc also started me on Adderall as well, like a year ago.. Now the previous doc I had for subs, who was a good doc, just too far away from where I moved to when I moved a couple years back he would ONLY prescribe suboxone, no matter what, unless you were a pregnant female, and while that pissed me off, having to pay out of pocket for suboxone (the generic white tabs) which were way more expensive without insurance than subutex... He was very liberal about prescribing me benzos with the subs.. he was the original doc to prescribe me klonopin in the first place, 5 years or so ago.. he also had me on 5mg a day of them, while my current doc, will not go over like 3-4mg a day, wont just give me 4mg even though I really should be on 5mg at least, but she is cool in different ways... had no problem with switching me to subutex, when I told her I had no insurance... and also didn't mind at all putting me on Adderall when I asked, after being diagnosed with ADHD, after living my whole life without any knowledge I really had it.. My old doc prob would have done the same.. but I never asked.. My current doc even knew I was an ex-cocaine user, for failing multiple random UAs when I started going there... she still gave me Adderall IRs off the bat, even knowing I used to abuse stimulants which REALLY surprised me!
Now, sorry I went a little off topic with the whole Adderall thing, as I know your question has nothing to do with that.. My point is, some doctors are much more laid back about prescribing benzos with subs.. some aren't.. My first ever sub doc, who knew I had crippling social/general anxiety wouldn't even THINK about putting me on benzos.. he told me I had a death wish asking to be prescribed something other than SSRIs, which I tried tons of different meds of that class for anxiety.. and none helped! He also gave me no option of maintenance or a taper with the suboxone he had me on, and tried to cut me off in like 2 months entirely.. starting me at like 16mg or some stupid high dose, and cutting my dose in half each visit every 2 weeks.. until I was at 2mg a day, it didn't help.. I tried telling him it wasn't curbing my cravings like 8mg was, and he didn't listen.. that resulted in me relapsing on oxy, even worse than I was before going to see him.. worst sub doc ever! He had all 1 star/F ratings on google when I typed his name in..
So look up sub docs in your area on google, or on whatever search engine your prefer... and see if they have any ratings, which one has the best, and also isn't too expensive.. My current doc is one of the cheapest sub docs in my area, and is an all around great doc in my opinion.. not solely because of what she prescribes me, because she actually knows who I am and gives a fuck about me... my other doctors, including the previous one who started me on kpins, just saw me as patient #50 (or whatever it was that day) of the day... not really interested in my life at all.. just asked how I was, gave me scripts, and I was out in 10 mins.. I didn't really love that tbh. So yeah.. before just going to any sub doctor, look into them first.. trust me! Also, klienerkiffer is correct, a lot of this question you asked, has to do with what state your in.. I live in FL.. its really kind of random here... some of my friends go to sub docs who wouldn't think of ever putting them on both suboxone and any benzo.. some will only give them like 0.5mg of kpin a day, even though they feel they need at least 2-3mg a day.. some don't mind at all mixing the two, like mine now, and will gladly give you what ever it takes to keep you off the streets and off dope/opiates.
Good luck to you!