I will be working on the best definition of morphosyllabic for a while. Here is a start. Chinese characters each represent a single syllable, and in the vast majority of cases a single morpheme (from the Zompist ).
Here is what John DeFrancis has to say.
Defrancis first used the term in the second last paragraph of his chapter in The Chinese Language: Fact and Fantasy, 1984.
The Chinese system must be classified as a syllabic
system of writing. More specifically, it belongs to the
subcategory that I have labeled meaning plus-sound
syllabic systems or morphosyllabic systems.
(Visible Speech, 1989, p.115 - 116)
Some linguists find the term awkward and substitute the term logosyllabary. (World's Writing Systems, P.T. Daniels, 1996, p.4)
Either of these are a million times better than the noncomital term sinogram, favoured by some. That term googles best as a medical procedure which I refuse to dignify with a link!
As for the term ideogram, well, I for one have always liked to read John DeFrancis books on Chinese and chapters of his various books have been made available at Pinyin Info. I would recommend The Ideographic Myth as a pleasant Sunday afternoon read.
Morphosyllabic is also the term prefered by those who write about reading theory and compare effects of dyslexia across different scripts, so it has my vote.
I was using the term morphosyllabic, (in a dialogue with myself), in the late 80's when I was looking at other syllabic scripts that used additional symbols to differentiate what would otherwise be homographs. This term fits me like an old slipper, and awkward as it may feel to others, I think I can guarantee that a sinogram would be worse.