Typically a normal half lease is half of board in exachange for half of the riding time, but every arrangement is different.
For example, I lease my horse for $250 a month for 3 days a week, I let me leaser ride more at no extra charge if I'll be away or can't make it. Board cost me $650, shoes $175 every 6 weeks and supplements are another $50 a month. The amount he pays doesn't even begin to cover half of her expenses.
Now there is woman in my area who wants $200 to lease her horses, which are in her back yard, 3 day a week plus farrier bill and half of supplements. Personally, to me, sounds a bit complicated PLUS expensive!
To me, sounds like you're getting duped. You can probably find something less expensive/complicated easily.
Ps, there are a few advantages to leasing. 1. You don't own! Walk away at any time, whether you have family issues going on, your riding ability changes, or you just don't like that horse. 2. You pay for the days you ride. Due to my schedule I only rode *maybe* 5 or 6 times, I still had to pay for the other 25 days I didn't ride her. So, about $550 worth.