Can I Refinance My Interest-only Loan With A Conventional Loan?

That depends on two main points, what is your credit, and is your home worth more today than it was when you got your interest only loan?
If you have excellent credit; 720 median score or higher, then you are in luck and can borrow up to 125% of your home's value... the draw back?  a higher interest rate.  Now, if your house is worth more than it was at the time you got your current loan, and you only want to refinanace with no cash back, the magic number you are looking for is 80.  That's right.  If what you currently owe is on 80% or less of what your house is worth, then you can easily finance that amount with no fear of private mortgage insurance (PMI) or high rates.
Hope this helped.  My advice, get an appraisal. They are good to use for 60days by most companies. Do not go with a company that pays for your appraisal!  Then they own it and you'll have a hard time backing out of the loan before closing if they bait and switch on you.  Get one yourself so that you own it and can take it to who ever and how many ever finance companies you want.