My husband and I have recently formed a Limited Liability Company
which is considered to be a partnership for tax purposes.  We require
start-up capital, and we're considering a "personal loan", as they're
much easier to get than start-up business loans.  My question is this:
 if I take out a personal loan in my name, inject that money into the
business, then pay it back out of the business's funds, will those
monthly payments be considered my "income" from the partnership (and
therefore be subject to self-employment tax)?

No.  You should develop a relationship with a CPA so you can get these
types of questions answered during the course of your business.  I am
sure there will be others.

Only the interest you pay to yourself, if any would be income.  And it
is not a wage and therefore there are no payroll taxes.  Thinks of it
as being no different that buying a CD or a bond and earning interest.