My advice is to bill hourly whenever you can because the client won't express everything they want done initially. This is because they don't know everything they want until they have part of it. Just think about doing a job for yourself and how many times you realize how much more you need to do after part of it is finished.
I do some web design. I wouldn't pay hourly for an initial website design & implementation. If you've got a designer/developer that is incompetent (or just out of practise) then they are going to take a lot longer and so cost more. Agree a price, technical problems are the designers problem.
Admin stuff takes quite a lot of time in a small business, in my experience (3 small businesses so far). Also just doing the design implementation stuff isn't enough - you do have to get out and win the work. 50:50 sounds about right IMO.
That's assuming he is doing inital design (graphical prototype, you'll need usability input here) and preparing graphical elements for the coded pages; as well as the up front promotion and sales.
Kinda depends on what sort of sites you're doing. A heavy app with lots of DB design or lots of scripting would need more weighting towards you. A simple graphical "this is us" site the weight is more towards him (and you're probably better outsourcing the coding of that sort of thing anyway).