My ex-husband and I have two properties, both under joint names. I live in my property `123 Sred Road¿ and he lives in his property `456 Cimber Road¿.

You have stated that there is a consent order.  This would indicate a stipulation of settlement which the Court converted into an enforceable order by "So Ordering" your agreement.  This is now enforceable as any Court Order with mechanisms that could be as harsh as contempt of Court for failure to comply. The provisions you cite require a new deed to be executed for each property transferring you one property and you ex-husband the other property.  This deed and accompanying transfer documents required by both the State and local municipalities should be prepared by an attorney and you should provide that attorney with the relevant documents from your divorce. The consent order states that the transfers are to be subject to the outstanding mortgages and nothing you provide requires the properties to be refinanced or modified to remove anyone from the mortgage.  You will absolutely need his consent and signatures for any such transfers of property which would be the first step before refinancing the property.  Once the property is in your name, you could then refinance with any mortgage product you desired as long as the prior loan was paid off.