I myself have never heard of "co-compounds" before but here's what I've been able to find.
At first, a note on terminology. There is a coordinate compound and there's also a co-compound. These are two different things.
A coordinate compound (sometimes called coordinative compound) is usually understood as compound with two heads (e.g Fabb 2001: 67, Scalise and Bisetto 2009: 46). Under this analysis, "bittersweet" is an endocentric coordinate compound (with mixture interpretation, Lieber 2009).
A co-compound is a "natural word-like unit consisting of two or more parts which express natural coordination" (Wälchli 2005: 1). In other words, those coordinated items are closely related in meaning, they are expected to co-occur, they form a conceptual unit, and the whole meaning is more general than the meaning of its parts (Wälchli 2005: 1, 5).
husband and wife, eat and drink, hands and feet etc.
That is why the following are not co-compounds, although they are coordinate compounds:
southwest, blue-green (no coordination)
poet-doctor (no close relationship)
twenty-two (different hierarchy)
OED defines bittersweet as "sweet with an admixture or aftertaste of bitterness. fig. agreeable or pleasant with an alloy of pain or unpleasantness." As you can see from this definition, the parts, bitter and sweet, are on different hierarchical levels; thus, "bittersweet" is not a co-compound.
For further discussion of co-compounds, see Wälchli 2005.
Of course, there are many other classifications of compounds; e.g. under Haspelmath's classification, bittersweet is an appositional compound and not coordinative (Haspelmath and Sims 2010: 141)/copulative (Booij 2007: 80) etc. Next time you ask a question, please define the terms you use.