(1) Background: Despite the verified relationship between relatives’ characteristics and individual suicidal ideation, few studies have discussed the role of family members and lineal consanguinity independently according to whether they live together with the individuals or not. (2) Methods: The data in this study were collected in November 2019 and identified rural adults over 18 years old in Shandong as the survey objects, with a total of 879 valid cases included in this survey. Logistic regression analysis was employed to examine the risk factors affecting adults’ suicidal ideation and differentiate the effects of a family member and lineal consanguinity’s physical and mental health. Relatives’ physical and mental health were estimated by three aspects: whether they were suffering from chronic diseases, mental illness, or alcoholism. (3) Results: The study showed that a family member’s physical (OR = 2.303, p < 0.01) and mental health (OR = 5.877, p < 0.05) was related to suicidal ideation, but the association between lineal consanguinities’ physical and mental health and suicidal ideation were not supported. People over 40 years old (OR = 6.528, p < 0.05), from only-child families (OR = 4.335, p < 0.01), with household indebtedness (OR = 2.992, p < 0.001), or difficulty falling asleep (OR = 3.165, p < 0.001) had risk factors of suicidal ideation. (4) Conclusions: The physical and mental health of individuals’ family members are related to their suicidal ideation, and their lineal consanguinities’ physical and mental health are not related to suicidal ideation. These findings imply the different associations between family environment, genetic factors, and suicidal ideation. Family members’ health should be considered as a factor to prevent and control suicidal behaviors, including suicidal ideation.