When should my husband sponsor me?

The asylum roll-back is already reflected on your husband's green card (this is why it states "Resident since 2010" while, in fact, he received his LPR status in 2011), and he will not be eligible for naturalization until 2015. If he files a petition for you now, you will become eligible for an immigrant visa in about 2 years. It appears that, either way, you cannot get a green card before 2015. I would not, however, recommend to postpone filing the petition until your husband becomes a U.S. citizen: processing of an immigrant petition by the USCIS and by the National Visa Center of the Department of State takes well over a year; so it should be started as soon as possible. If your husband becomes a citizen before your priority date is reached, he can notify about it the agency that will be handling the case at the time, and have the case upgraded.

When a person's asylum is approved, they are issued a "white card", then they are eligible to apply for "green card" after 1 year, however, when the green card is issued, the person is given 1 year credit. So you count 5 years from date of issue on the green card to apply for citizenship. In other words, if your husband's green card issuance date (which is printed on the green card) is 2010, then he's eligible to apply for citizenship in 2015. I highly recommend he files your petition (Form I-130) immediately so you can hold a priority date. Your visa will be available in 2 years as a spouse of an LPR, so you should be able to come in 2015, and possibly even before he's eligible to apply for citizenship, which is never guaranteed.