All push drills had a proprietary bit type. Either notched or a spline shank. IIRC you can buy adaper chucks but I think that would introduce a lot of slop in the alignment which is the main advantage of a push drill to me.
That said, most of them, at least the MF ones I have that use splined bits, will also hold standard twist bits in a limited range. I can’t recall that range right now though. I know they won’t go all the way down to fully closed though and IIRC the max size is around 1/8”. So if I was to guess I’d say like 1/16-1/8 inch twist bits.