Family conflict and family functioning were regarded as changeable factors associated with complicated grief (CG) and major depressive disorder (MDD) in the bereaved families of patients with advanced cancer, although the evidence is limited. We explored the family functioning associated with CG and MDD developing either independently or co-morbidly in the bereaved families of patients with advanced cancer who died in palliative care units (PCUs). This study comprised a nationwide cross-sectional questionnaire survey of bereaved family members of cancer patients who died in Japanese PCUs participating in evaluation of the quality of end-of-life care. A total of 529 questionnaires (69.2%) were returned, and we analyzed a total of 458 responses. A total of 14.2% of participants were considered as having CG, 22.5% as having moderate to severe depression, and 9.6% as having co-morbid symptoms. Multivariate logistic regression analysis revealed that many family members insulted or yelled at one another (odd ratio [OR]: 2.99, p = 0.046; OR:2.57, p = 0.033), and conflict regarding what is meant by a good death (OR:3.60, p = 0.026; OR:4.06, p = 0.004) was significantly positively associated with CG, MDD, and co-morbid symptom. Specific family conflicts may increase the incidence of CG, MDD, and co-morbid symptoms in the bereaved families of patients with advanced cancer. Our results may encourage health care providers to approach discussions about end-of-life issue with the patient and their family in advance, especially focusing on what is considered a good death for the patient, which may prevent or resolve the family conflict.