Few studies have focused on sleep apnea and substance use disorders with co-occurrence of anxiety disorder and depression. This study included a total of 270,227 adults, 9,268 with co-occurrence of anxiety disorder and depression in the past year, from the combined 2008–2014 National Survey on Drug Use and Health (NSDUH) data, which are the latest datasets with measures of anxiety disorder and sleep apnea. Weighted multinomial logistic regression analyses were used to estimate the associations between anxiety disorder and depression and their co-occurrence. Comorbidity was highly prevalent: 40.4% of those with depression also met the criteria for anxiety disorder, whereas 51.8% of those with anxiety disorder also met the criteria for depression. The prevalences of anxiety only and co-occurrence increased from 2008 to 2014. The prevalences of anxiety disorder only, depression only, and co-occurrence of anxiety disorder and depression in individuals with sleep apnea were 4.4%, 12.9%, and 12.2%, respectively, and the prevalences in substance use disorders were 6.4%, 9.4%, and 10.7%, respectively. The results showed that sleep apnea, substance use disorders, and nicotine dependence were significantly associated with increased odds of anxiety disorder, depression, and co-occurrence (all p values < 0.0001). Furthermore, several chronic diseases (asthma, bronchitis, hypertension, and heart disease) were associated with the co-occurrence of anxiety disorder and depression. These findings suggest clinicians and other healthcare providers consider screening for depression and anxiety with sleep apnea and substance use disorders for improved therapeutic outcomes.