Background Impairments in executive function and social cognition are highly prevalent in individuals with an alcohol use disorder (AUD). Some studies show that similar difficulties are displayed by individuals with a positive family history of AUD (FH+) compared with individuals with a negative family history (FH‐). Yet, no studies have jointly investigated cognitive and affective theory of mind at the behavioral level. Moreover, some studies show preserved executive and socioemotional functioning in FH+ participants. One possible explanation for these divergent results is that FH+ individuals are cognitively heterogeneous. In this study, we examined the frequency and co‐occurrence of difficulties in executive function and social cognition among FH+ individuals at the individual level. Methods Sixty FH+ and 60 FH− participants matched on age, sex, and education level were included. They completed tasks assessing executive functions (Stroop, Trail Making Test) and affective and cognitive theory of mind (Movie for the Assessment of Social Cognition). They also completed self‐report questionnaires measuring impulsivity, alexithymia, and empathy. Single‐case analyses assessed the proportion of FH+ participants with difficulties in executive function and/or theory of mind. Results FH+ individuals exhibited difficulties in response inhibition and made more errors during theory of mind processing, indicating an absence of mental state representation, compared with FH− individuals. In the FH+ sample, 53.33% had executive function and/or theory of mind difficulties. Those with lower theory of mind scores reported higher alexithymia and lower empathy on self‐report measures. Conclusions FH+ individuals display heterogeneous executive function and theory of mind abilities. Given that they mostly occur independently of one another, executive function and theory of mind difficulties may be distinct vulnerability markers in AUD.