You should not take this refinance. The bulk of your debt ($52,000) is already at a very low 3.75% rate. In order to refinance some higher interest debt, you would be willing to increase both the interest rate, and the length of the payoff. Just that part of the refinance costs you up to an extra $18,000. I don't know the exact amount because you haven't specified the length of time remaining on your current mortgage so I'm making some educated guesses.
Now for the loans you would be consolidating. You haven't specified the amounts and the interest rates of these other loans, but we can assume they are high. Your new loan amount would increase by $14,000, so we do know that if you refinance them at 3.875% over 30 years, you will be paying $23,700 to retire those debts.
So to sum those two figures, you would increase your debt payments somewhere in the range of $40,000 to pay off less than $14,000 worth of credit card and student loan debt.
You could certainly pay back the value of those CDs after retiring the debt for a much lower cost. This would be my first recommendation if you have the discipline to budget and repay your savings after your debts are gone. You could also consider opening a home equity loan rather than refinancing your lower 3.75% rate. The home equity loan would probably cost a little more per month than this total refinance, but you would be out of debt much sooner.