"economic burden" VS. "financial burden"--are they interchangeable?

In almost all contexts, the two terms are interchangeable.

There are, however, some contexts in which, in considering the economic costs (burdens) of something, one wants to take into account not only the burdens of paying for it, but all the burdens that can be measured in economic terms, including those that don't involve actual payments. To develop the OP's example, suppose that some plumbing repairs need to be carried out on the young couple's house, and that a plumber would charge £100 for that work. To save the money, the owners do the work themselves. Their work has a definite value, expressible in economic terms, that is £100, even though it was not paid for. In such a case it can be said that the £100, the economic value of the work they have done, is a part of the economic burden of having the house, even though it is not a part of the financial burden.

Again, the significance of all this is likely to be appreciated only in certain theoretical contexts. Most young couples simply ignore the economic value of the burdens such as doing plumbing repairs on their own. In most everyday contexts, financial burdens and economic burdens are thus interchangeable.