The most common scenario is that according to the analysis used by your primary mortgagee company, you borrowed more than 80% of the value of your home. This LTV (loan to value) calculation drives an important variable: the need for PMI (mortgage insurance) which is required if your loan is over 80% loan to value.
I presume that you had very little to apply to the purchase price (or less than 20% of the value of the home), which is what made the 2nd necessary. Very interestingly, congress just recently made PMI tax deductible. If you want to read more about this, Bill was recently interviewed on the subject: http://www.jsonline.com/story/index.aspx?id=563996
Basically, now it is possible, but not guaranteed that you can benefit from having a single larger loan combined with PMI, as opposed to the traditional piggy-back loan (which is what you got).
You can always apply for a new loan, or a home equity loan, but it will be at a very high LTV, which means you will need perfect credit and a good income stream.
You can apply with Bills' approved lenders by following this link:
Bills.com has many providers who can help you on this, if you want to apply just follow this link:
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