Add all of the salsa ingredients to a food processor and pulse until blended but still a little chunky. Pour the salsa into a medium saucepan and warm over medium heat for about 10 minutes.
While the salsa is heating, place the poblano peppers on a baking sheet lined with foil. Place the baking sheet on the highest rack in the oven and broil on high for 15 minutes, flipping every 5 minutes.
Once roasted, remove the peppers from the oven and place them in a sealed plastic bag for 10 minutes to steam. Turn on the oven to 375°F.
After 10 minutes, remove the peppers from the plastic bag. Peel off as much charred skin as you can, but don't worry if there is a little still on the pepper. Cut a slit in the side, and remove the seeds and top stem. Repeat with all of the roasted peppers and then dice into ½" pieces.
Shred and crumble the 3 kinds of cheese and mix them together in a medium mixing bowl.
Pour the warm salsa into the bottom of the baking dish. Take half of the chopped roasted poblanos and spread them out over the salsa in a layer. Top the peppers with half of the cheese mixture. Repeat the layer with the rest of the poblanos and cheese.
Bake the dip in the oven at 375°F for 20 minutes. Turn the broiler on high and brown the top of the dip for an additional 2-3 minutes. Remove the dish from the oven, allow it to cool for a few minutes and then serve it immediately with your favorite tortilla chips!