What sort of job opportunities are available to someone who double majors in computer engineering and aerospace engineering?

Well for one, the same job opportunities as someone with a major in CompE, or a major in AE. Given that the job opportunities for CompE alone are immense, that's not a bad position to be in.

There will be some niche areas that take advantage of the overlap.

If you're looking specifically for defense contracting or something similar, there is a rather lot of software written for planes, rockets, etc now (e.g. the Joint Strike Fighter). Now whether or not you specifically want to work on that is a different question (e.g. there have been... problems... with the software dev for JSF, at least I've heard 2nd hand from people at lockmart).

I graduated with CS and two separate engineering degrees, and when interviewing for software jobs the engineering degrees did not help at all from an interviewing standpoint. On the other hand, maybe it looks impressive so maybe it gets you snapped up by recruiters (this would be a good question to ask some recruiter).

There are some degree combinations which can be really good. Comp Sci and some sort of biomed degree can be quite useful. Any engineering and a J.D. (law degree) is a canonical choice if you want to go into patent law. Etc etc. It depends on what you want to do. If you're dead set on working on plane software or rocket software or something, CompE & Aero sounds like a fine choice. Worst case you have a multitude of fallback options with just CompE.

My degrees are in Civil Engineering (concentrating in earthworks and construction) but I work in Telecomm now (for the last 20 years or so). However, I interact with IT on about a daily basis. While I am not doing the actual coding or deployment of hardware, I am very involved in the development of systems, as the voice of the customer (The customer in this case being the engineering people that use the systems that IT is developing). Most of my understanding of CS I learned on my own. Either through ad hoc learning, one off courses, or interal training on either technology or methods (I just attended an 8 hour DevOps session last week for example). Having the ability to interact with and talk to IT with a good knowledge of what their job entails makes my job a lot easer, and makes me a more valuable employee.

So, my take on the questions is, a background in CS will definately help. If you can manage a dual major, that is great. If not, I still suggest that you have a good understanding of CS, no matter what engineering field you are going into.

-dave