The problem you have here is not that you're unemployed and your prospective partner isn't (that actually hurts you, as it decreases your opportunity cost). Rather, the problem is simply that your partner isn't working for the company.
The tricky issue here isn't the split. If you think your partner is going to add significant value to the company (and: you clearly do), stop obsessing about the split, because how you carve up equity isn't going to change your outcome nearly as much as how well you two work together. Both negotiating for a better split, and, worse, executing the company as an unequal partnership are going to cost relationship capital. Save that capital for something that really matters.
The tricky issue is vesting. DO NOT ENTER A PARTNERSHIP WITHOUT VESTING. Anyone who gets equity, YOU INCLUDED, needs to be on 4-year vesting. Since you can't really "vest" someone who isn't even working for the company, you have a bigger problem than the split.
My suggestion is, don't offer your prospective partner any equity until they start. That default starting equity, while significant, won't be equal to yours; it'll be, as Joel Spolsky puts it, "second stripe" equity. (Joel's stripe examples are 50/10/10/10/10/10, but you'd obviously change that; perhaps 30/20/10/10/10/10).
At the same time, offer them an option to purchase equity equivalent to yours (ie, to buy 5% of the company). The price of that option should capture the value of the time you spent working on the company PLUS the added risk you took; think of it as a premium on your salary to prevent the partner from waiting- and- seeing how well things go before joining up (if the cost of the option was just your salary, it would be dumb for them to pay it until they had to, and they'd be disincentivized from joining).
Be aware that your prospective partner is probably going to balk at this, in which case, oh well; there's lots of ideas out there. If you're not in a position to amicably walk away, no-harm no-foul, you have no business negotiating at all.