Yes, the Xbox One can play CDs and will support DLNA streaming
Sony announced some details on things the Playstation 4 can and can't do, and I had sent a question over to Microsoft about whether the Xbox One would be able to beat those features. I've just now received an answer and, yes, the Xbox One can play audio CDs.
The system is also DLNA compatible, and they're in the process of being certified. As for mp3 playback… well, that's kind of a mixed bag. The system is a Play To receiver, so you'll be able to stream your content to the Xbox One using any Play To supported devices such as a Windows 7, 8, or 8.1 enabled PC, Windows Phone, etc.
You'll also, of course, be able to stream music through an Xbox Music Pass subscription.
So it doesn't seem like there is going to be a way to simply import your music files, but you will be able to stream the content you already own, hopefully use it in custom mixes for your game, and the device will be DLNA compatible. Audio CDs, for the people who care, will be supported.
So there you go.