This dip is runny right off the stove (great for drizzling over nachos or tacos), then thickens as it cools (perfect for dipping). It will eventually get very thick, so consider serving it in a slow cooker set to warm.
In a small saucepan combine American cheese and half-and-half. Cook and stir over medium heat until mixture is smooth. Gradually whisk in the Monterey Jack cheese until smooth. Stir in the green chiles, jalapeños, and juice. Cook and stir for 2 minutes more. The Queso will be thin at first, but thickens quickly as it cools. (To maintain a dipping consistency, reheat occasionally or serve in a small slow-cooker or fondue pot.)
Look for white American cheese at the deli counter.