Thicke died in December after suffering a ruptured aorta while playing hockey with Carter.
"Happy Birthday to my angel ❤ #2016 joint birthday celebration, they say 2 Pisces are internal soulmates ?? You are so missed my love......," Tanya wrote alongside a sweet image of her and Thicke celebrating their birthdays last year.
Carter, meanwhile, shared a cute throwback pic of himself riding on his father's shoulders.
"Missing you and our times together extra today," he wrote. "Enjoy your birthday margarita and rhubarb pie up there, relaxing in your robe watching ESPN. You are and always will be the man. Happy Birthday Pops ?."