This is one of those classic "opportunity cost" questions: if you spend money on one thing, you cannot use it on anything else. Given your job uncertainty and the fact that you're both working for the same employer, definitely beef up your emergency reserves to, say, 6 to 12 months of expenses. If you can do that and refinance, that would be great. Perhaps some household expenses can be reduced to make the numbers work so that this is not an "either/or" decision.
Consider doing some stock investing in a tax-deferred retirement savings plan so you can buy shares "on sale." In addition, there are tax advantages. The amount that you contribute can be deducted on your federal income tax return and your savings plan contributions and earnings grow tax deferred until they are withdrawn.
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