Strictly speaking, monogamy means having one partner. So how do three-ways fit into this definition? Can couples have three-ways and still be monogamous? I suppose the answer lies in "how significant" the other member is to them, and what they deem to constitute infidelity.
If the third party is, as suggested, not significant, that could be construed as meaning the partners still have only one partner or, rather, one significant partner, and are, therefore, still monogamous. Many birds are considered monogamous, but DNA tests on offspring show that this is not 100% so, that there's often a little fooling on going on, but the couples still maintain stable relationships and are, therefore, be considered monogamous.
In the case of birds, the male bird is unaware his partner has cheated, just as his female partner is unaware of his secret philandering with another female. This can work for birds and some very trusting humans, but is often complicated in humans by gossiping friends or private detectives. In this case, we look to what they consider constitutes infidelity (cheating). If the couple agrees to strict monogamy (faithfulness), then any transgression is verboten. If they make some other agreement, like three-ways, then that's okay. In other words, infidelity consists of any violation of agreed-upon terms. Everything within those terms is acceptable, even though these might be considered outside the bounds by other couples.
By this reasoning, three-ways would be considered "monogamous" as long as this is agreed upon by the couple and any third party is "insignificant" to their relationship. However, this does not always mean it's wise. Regardless of agreements, human emotions are not always so straightforward or predictable as to be corralled within artificial boundaries and those insignificant third parties can turn out to be all too significant.
