Since it's not tagged united-states, I'd like to offer a more general advice. Your emergency fund should match the financial risks that are relevant to you.
The two main classes of financial risk are of course a sudden increase in costs or a decrease in income. You'd have to address both independently.
First, loss of income. For most, this would simply equate to the loss of a job. How much benefits would you expect to get, and for how long? This is often the most important question; the 6 months advise in the US is based on a lack of benefits.
With two incomes, you're less likely to lose both jobs at the same time. That's a general advise, though. If you both work for the same employer, the risk of losing two jobs at the same time is certainly real. Also, in countries with little protection against dismissal (such as the US), the chance of being layed off at the same time is also higher.
On the debit side, there are also two main risks. The first is the loss or failure of an essential possession, i.e. one which requires immediate replacement. This could include a car, or a washing machine. You already paid for one before, so you should have a good idea how much it costs.
The second expenditure risk is health-related costs. Those can suddenly crop up, but often you have some kind of insurance. If not, you'd need to account for some costs, but it's hard to come up with an objective number here.
The two categories are dependent, of course. Health-related costs may very well coincide with a loss of income, especially if you're self-employed.
Now, once you've figured out what the risks are, it's time to figure out how to insure against them. Insurance might be a better choice than an emergency fund, especially for the health costs. You might even discover that you don't need an emergency fund at all. In large parts of Europe, you could establish a credit margin that's not easily revoked (i.e. overdraft agreements), and unemployment benefits are sufficient to cover your regular cost of living. The main risk would then be a sudden lack of liquidity if your employer goes bankrupt and fails to pay the monthly wages, which means your credit should be guaranteed sufficient to borrow one month of expenses. (This of course assumes quite good credit; "pay off my car" doesn't suggest that.)