Background: Insufficient social support has been intensively studied as a risk factor of postpartum depression (PPD) among mothers. However, to date, no study has examined the role of informal and formal dimensions of social support during pregnancy with regard to joint maternal and paternal depression after birth. Aim: Study associations between insufficient informal and formal support during pregnancy and joint parental PPD. Methods: Using data from the nationally representative French ELFE ( Etude Longitudinale Française depuis l’Enfance) cohort study ( N = 12,350), we estimated associations between insufficient informal and formal support received by the mother during pregnancy and joint parental PPD in multi-imputed multivariate multinomial regression models. Results: In 166 couples (1.3%), both parents were depressed. The likelihood of joint parental PPD was increased in case of insufficient informal support (insufficient partner support: odds ratio (OR) = 1.68 (95% confidence interval (CI): 1.57–1.80); frequent quarrels: OR = 1.38 (95% CI: 1.19–1.60)). We also observed associations between formal support during pregnancy and joint parental PPD (early prenatal psychosocial risk assessment: OR = 1.13 (95% CI: 1.05–1.22); antenatal education: OR = 1.13 (95% CI: 1.05–1.23)), which disappeared when analyses were restricted to women with no psychological difficulties during pregnancy. Conclusion: Insufficient informal social support during pregnancy appears to predict risk of joint PPD in mothers and fathers and should be identified early on to limit complications and the impact on children.