Both of my kids did this when they were that age. It basically boils down to the kiddo does not have your (or your partner's) undivided attention and they want it. There are several ways to cure this behavior, or least I have been told there are. The one that work best for my family was the following procedure...
When we all came together we would devote a minute or two of our attention towards each of the children, starting with the youngest. Then we would start an adult conversation and the kids would either continue what they were doing or find something else to do.
9 times out of 10 this worked like a champ. If it did not there was usually something else going on and the kid(s) needed a bit more attention, so we would allow them that.
If the extra time did not work either, 99.9% of the time it was a power play from the kids to keep our attention. This would usually lead to secluded time (time out) for the child.
After a while the kids began to understand that my wife and I usually did not need more than 10-15 minutes to discuss whatever it was we needed to talk about, and stopped interrupting all together. If there was something they needed after we talked they would wait their turn. Emergencies aside of course.
My kids are a little older now but the practice of going around the room (usually at the dinner table, we eat early) and sharing a brief summary of the day's events stuck. I look forward to this 30-45 minute period everyday.
The big thing is whatever course of action you take, you have to be consistent. Kids are very smart and if they see a crack in the defenses, they will exploit it :)