Your profile page indicates your carrier is Verizon, just offhand (more about curiosity than relevance) do you know which carrier your friend is using? Also, is your friend able to receive SMS and MMS messages sent by you?
More specifically though, given that some MMS messages come through but others not, are you able to consistently receive SMS messages from them? If SMS is a problem too, there might be an issue that needs to be fixed in the Settings menu of your texting app. If SMS messages are not a problem, it could just be a matter tied to how different carriers have arbitrarily set different file size limits to MMS transfers -- if your friend has similar issues sending MMS messages to others too, they might want to scale back the default resolution of their phone's camera app so the photos/vids aren't so large.