Rimes, 30, shared a photo on micro-bloging site Twitter holding Jake and Cibrian, 40, has his other arm around Mason, reported Us magazine.
Their family getaway comes just a few days after the pair announced that Vh1 is set to premiere their new show, "LeAnn & Eddie" in fall 2013/winter 2014 with six half-hour episodes.
The couple married in 2011, two years after they met and fell in love while still married to other people. The show will also feature Cibrian's efforts to co-parent Mason and Jake with his ex-wife Brandi Glanville.