Source: Defense to the Opponent’s Jacoby 2NT by Roy Wilson 
When your opponents use a Jacoby 2NT bid in response to a major suit opening, be very careful about entering the auction. Both of them have opening hands and they hold the majority of the points! With that said, you certainly want to consider bidding with very good distribution.
If you have about an opening hand you can expect your partner to have almost nothing. There just are not enough points in the deck for anything else. Still, there are times when you should consider bidding. Ask yourself about the vulenerability – is it favorable for your side? And if your partner does not provide you with a single trick is your sacrifice going to give you a better score than what they can make if they play the hand?
With a single-suited hand and a very long suit most people know what to do – preempt as high as you dare!
But what about two-suited hands? If you bid one you will hide the other and that’s surely where your fit will be found.
Consider this as a reasonable criteria for bidding: Do you have great distribution that will help overcome the high cards held by the enemy? Do you have a method to describe your two-suited hand to your partner? You do need to get him involved.
Most of the time you should carefully consider entering the auction anytime you have a decent two-suited hand.
The Other Major and a Minor
Suppose the opening bid on your left is 1 and after your partner passes your RHO jumps to 2NT, alerted as showing 4-card support with at least an opening hand. (The opener generally has several options they have agreed to, such as responding by bidding a singleton, etc.) This is your hand. The opponents are vulnerable and you are not.
Make an agreement with your partner that overcalling with a minor shows both the bid minor and the other major. Now you have given your partner the information where he can make a decision about a sacrifice at either 5 or 5. With this hand you would bid 3 showing both clubs and hearts.
If you don’t like this idea you can fall back on the Michaels Cuebid to show the other major and an unspecified minor, but the bidding may be at a level when next it is your partner’s turn to bid that he might be reluctant to ask which minor you hold.
Both Minors
The other possible two-suited hand you might hold would be both minors. The simplest way to show this hand would be to bid 3NT over the responder’s 2NT bid. Sure sounds Unusal doesn’t it?
You can also jump to 4NT to show both minors and that has both an advantage and a disadvantage: it takes away their ability to use Blackwood, which is a good thing, but it’s also a unilateral decision that commits you to the five-level without any chance for your partner to be part of the process. You certainly would want to use this bid if you had even more distributional values, perhaps a six-six hand!
What About a Double?
You could use the double to show both minors instead of bidding 3NT – The Unusual Notrump Double which would be a safe lead-directing bid. Or you might agree that it shows a three-suited hand with shortness in the opponents major suit, but the most frequent holding you will have is the one with both minors. Be careful, though and please remember that your partner is going to hold very few points!
And What About a Jump Cue Bid?
Your choice. It’s certainly a dramatic bid and probably the most forcing bid you can make, but I don’t know what kind of hand it shows – perhaps a highly unusual two-suited hand of some sort.