Hi Nina -- yes you can have an IVA ( if it is indeed appropriate) if you have equity in your home. Make sure your chosen IP explains equity VERY thoroughly.
If you are not insolvent, then an insolvency solution might be over the top to tackle the problem.
A lot will depend upon your definition of insolvent -- it is no longer strictly that you have less in assets than in debts. More, these days, that you have less coming in than you have going out on essential living expenses and debt payments.
My opinions are merely that .. opinions based on experience. Always seek professional advice.
IVA Completed 23rd July 2013 .... C.C. 10th January 2014
We have proposed IVAs where there was more equity than debt and they have been accepted. However, you would want to show that you cannot remortgage and agree to at least attempt one in year five. Get some free advice and hopefully someone will show you the right option.