I've recreated an example logo:

1. Keep GaryLang, White Group and Black Stroke Group shapes in separate layers.

2. Select GaryLang layer and Object > Compound Path > Make

3. Select Black stroked Group layer and Expand it. Then use Pathfinder Unite.

4. Make this layer too a Compound Path.

5. Make sure Group layer is above GaryLang

6. Select both GaryLang and Group and use Pathfinder Minus Front.

You should get desired result.

Another way of doing this using Shape Builder tool. Once you've performed Step 3 (Compound Path not necessary for this case), select both GaryLang and Group use Shape Builder tool. There's option to remove all unwanted shapes (Alt+Click). It will *become transparent.

I've recreated an example logo:

1. Keep GaryLang, white Group and black stroked Group shapes in separate layers. Let's call GaryLang as L1, black stroke Group as L2 and white Group as L3.

2. Select L1 layer and Object > Compound Path > Make

3. Select L2 layer and Expand it. Then use Pathfinder Unite.

4. Make L2 layer too a Compound Path.

5. Make sure L2 layer is above L1.

6. Select both L1 and L2 and use Pathfinder Minus Front.

You should get desired result.

Another way of doing this using Shape Builder tool. Once you've performed Step 3 (Compound Path not necessary for this case), select both L1 and L2 and use Shape Builder tool. There's an option to remove all unwanted shapes (Alt+Click). The black stroke will become transparent because actually it would be deleted along with L1 unnecessary parts.

Both methods might look confusing at start, so I'd suggest trying on simplest shapes to test it. Especially method 1. It worked for me, but you might need to twist a few steps a bit depending on your sub-text.