Home page to communicate two different services of equal importance

I understand that this could be a duplicate question, but I feel that none so far have answered mine.

My client has two services, and he wants one website essentially split into two sections which are fine because each one can be marketed separately to the correct audience and sites can always be easily divided, etc.

However, each service has its specific message, and the thing I'm struggling to understand is how the homepage (above the fold) can communicate two different ideas without confusing the user especially when viewed on a mobile phone.

Should I combined any shared qualities between the two and somehow create a single value proposition statement (maybe around the experience the companies offers on the whole) and place two buttons for each service directly underneath it?

To take this a little further we can introduce social media into this problem. You wouldn't create two of every social media account for each service; you would probably try to build a unified brand/message however you could.

So does that mean your homepage should take on the same approach?

I hope this isn't seen as a duplicate question and thanks to anyone who wishes to help me solve it. :)