My impression is that your friend is trying to profit from your hard work. I don't see the amount of time as being 50/50. So you need to factor in whether his contribution is worth the 50%. In my experience you'd pay 5% for an introduction. 15% - 25% for the invoicing, collecting, account management. So really depends whether the design work is worth 35% or more.
Another arrangement is that you get back to him and say, that if he makes the introduction, you take on the client and pay him a commission of 15% and bill the design work to the client and keep 15% for admin costs.
A partnership or company is the last thing that I would suggest. Too many things can go wrong over time. Believe me, it took me 4 failed companies before I realised that it's impossible to reconcile expectations, especially when people have jobs, social life and other ever-changing issues in their lives.
Good Luck!