Some examples of compound-complex sentences would be the following (note the underlined dependent clauses):
I invited Bruno to the concert, but he can only go if one of us gives him a ride.
Kaci has a bountiful vegetable garden, so she is always outside when it is sunny.
As soon as I heard the news, I called Nathan, and we made plans to celebrate.
I passed the test, but I would have gotten a perfect score if I had studied for the vocabulary section.
You can come pick up the cake, or if you would prefer, we can deliver it to you.