Hi Alex. I've been alerted you're seeking a better answer to this question. ;-) Please accept my apologies for not coming back to this question sooner – it got buried. :-/
No, in general you cannot make an early withdrawal penalty-free from a 403(b) account to use towards the purchase of a home. Withdrawals before age 59 1/2 are generally subject to the 10% early withdrawal penalty, on top of ordinary income tax.
Some 403(b) plans may allow for a loan, but the availability and conditions vary by plan. If you'd consider a loan, you should check with your plan administrator or your plan's Summary Plan Description – often available at one's company intranet or HR web site. (I do contract work for an HR consulting firm that assists others in building such sites, and SPDs are usually something made available for download in a "Retirement" or "Wealth" section of such web sites.)
Note that a loan from a 403(b) would need to be paid back into the plan over some period of time, e.g. 5 years, though I have come across examples of some plans that do permit a longer pay back period of 10, 15, even 30 years if the loan is used for a home purchase. But consider this article: The 403(b) Loan: The New Debtors Prison?
Finally, to your last point: Yes, if you have an IRA, there are rules permitting withdrawal of up to $10,000 penalty-free for use towards the purchase of a first home. See page 53 in IRS Publication 590. There's also a good article at Fool.com: All About IRAs - For First Time Home Buyers.
Such a withdrawal from a traditional IRA remains subject to ordinary income tax. If have a Roth IRA, you can withdraw free of income tax but you need to pay attention to the Roth IRA 5 Year Rule.