From the information you've provided, this sounds like a VERY bad idea.
We bought the house at 287,000 ... with 3.5% down from our savings.
In my opinion, if someone can only afford to put down 3% on a house, they shouldn't be buying one.
Unfortunately most of the emergency fund is gone...
Abort, abort, abort! What happens if one of you loses a job, has a medical issue, car breaks down, house needs a new roof, ect.
If you don't have an emergency fund, you have no business buying a $300,000 house.
We hope to refinance in about 3 months with a 40,000 lump sum towards the principal (which we will be paying back in monthly installments interest free to my partners parents)
So you are going to have two sets of closing costs within a 3 month time span? How much is that going to cost you?
As someone else pointed out, it doesn't look like the $40,000 would get you enough equity to eliminate PMI.
Lastly, do you really want a $40K personal loan hanging over your head for the next several years, especially with no emergency fund cushion?
The estimate for mortgage/PMI/insurance/etc is $1690 a month...We currently rent at $1,000 +utilities monthly in the same general neighborhood.
Are your taxes factored in to that estimate? How about regular household maintenance/repairs? I'd add 10% for that. Even if you don't have a major repair (roof, plumbing, ect) for a few years, every house requires ongoing maintenance (lawn work, landscaping, painting, ect) and all of the tools needed for these tasks.
I would advise you to bail on this deal ASAP. Buy a place after you've saved 20% IN ADDITION TO an adequate emergency fund.