Here are a couple of links.
Mira, x-ray photo on the page:
http://www.astronet.ru:8104/db/xware/msg/1205472
And some diagrams, including a "contact" binary. We're both right. Not sure if the enveloped companion can be
a white dwarf, but could a white dwarf strip off a red giant's gas layer to leave two white dwarfs?
http://www.astro.psu.edu/users/rbc/a1/lec16n.html
could a white dwarf strip off a red giant's gas layer to leave two white dwarfs?
dunno - I'm just an interested dilettante when it comes to stuff like this.