Old-school etiquette would be: one person writes, same person signs, with all recipients mentioned. In your case, that means the note would be to MIL, from you, signed by you, but mentioning your DH's gratitude / excitement in the note.
When you think about it, two signatures doesn't totally make sense, because the person sending the gift will know you didn't both actually write the note. One handwriting, one voice, after all, plus your DH's thankfulness can be conveyed in a sentence or two in the note, rather than by his signature. Still, I doubt very seriously anyone would fault you for having two signatures - but it's just an unnecessary extra step IMO.