It's interesting that the term jealousy (and labels such as "green-eyed monster") is used without definition. Jealousy is not quite the same as envy. Both are complex emotions and have somewhat different origins. In fact, both crop up in the LS and it's worth recognizing the underlying fears.
Jealousy is often tied into fear of loss (of partner to another), sense of betrayal, uncertainty and even loneliness.
Envy is often tied into fear of inadequacy/inferiority and simultaneous resentment of some other person even while trying to assume some of their characteristics.
The opposite of jealousy is compersion, i.e. finding joy when your partner finds pleasure with whomever. Shifting the balance from jealousy to compersion requires a firm and maybe unshakeable belief in the durability of the partnership--knowing that s/he is the object of true and unshakeable love. That's a key conversation to have early and often in the LS--what is unshakeable and how perceived risks are going to be managed. Actions need to reinforce that conversation.
The opposite of envy is contentedness. In the LS, it is a blend of self-confidence and self-acceptance. In any collection of persons, there will always be someone else who is (choose one or more): taller, slimmer, firmer, flatter, bigger breasts, perkier breasts, tighter pussy, cums faster, cums slower, longer cock, thicker cock, more stamina, more responsiveness, deeper eyes, better kisser,... We are also attracted to different-from-what-we-already-have. That self-confidence and self-acceptance comes from within but within a partnership/marriage benefits from strong, regular, heartfelt reinforcement. Each of us has imperfections. We are often our own harshest critics. That can easily get magnified in an asymmetric swinging situation, especially where one partner has found a playmate and the other is not finding the chemistry/sparks.
Drama -- there's lots of it in the LS--is most likely to ensue where envy and jealousy start feeding off of one another: a feeling of envy towards a rival can significantly intensify the experience of jealousy.Sort of like gasoline and a match.
Perhaps there is a strategy for couples to deal with the these complex emotions. First, there has to be a willingness to be vulnerable--to be able to say "I am afraid". Second, there has to be a willingness to accept imperfections and even celebrate them. Those can be acknowledged and practiced outside of the LS. We would argue that they are foundational to a strong relationship. Being able to say "I am afraid of loss/abandonment or I am afraid of being inadequate" are essential first steps to dealing with jealousy and envy, respectively. As for imperfections, we all have them. We all acquire more. Some are physical, some are emotional, some are spiritual. Some are repairable, some are worth addressing. Those that are both are worth working on. Those that irreparable or insignificant must be accepted, and it's up to each of us how graceful we want to be about it.
As an aside, it's worth thinking about the age-old question, "How do I get my spouse interested in the LS?" Perhaps the better question is "how do we prepare our relationship for these negative and complicated emotions?" Once those emotions are honestly addressed, it's much easier talking and taking the LS adventure.