People with concomitant human immunodeficiency virus (HIV) and tuberculosis (TB) have an increased risk of hepatotoxic reactions due to antiretroviral therapy (ART) and anti-TB therapy (ATT). Concomitant hepatitis B virus (HBV) in these patients may lead to poorer health outcomes. To assess liver enzyme levels and immune response in adults with HIV, HBV, and TB, data from 300 antiretroviral-naïve people living with HIV (PLWHIV) were analyzed. The prevalence of HIV/HBV (cHIV/HBV) and HIV/TB (cHIV/TB) was 28% (95% CI: 23.0–33.4) and 10% (95% CI: 6.8–14.0), respectively. HIV/HBV/TB (cHIV/HBV/TB) prevalence was 5.3% (95% CI: 3.1–8.5). There was a statistically significant difference between the groups of participants in HIV viral load (p = 0.004), hemoglobin levels (p = 0.025), and body mass index (p = 0.011). A larger proportion of cHIV/HBV/TB participants (37.5%) had an aspartate aminotransferase to platelet ratio index (APRI) score ≥0.5 (p = 0.013), a lower cutoff for significant liver fibrosis. Immunological non-responders (CD4+ T-cell count <20% gain and HIV viral load <400 copies/mL at 6 months) were observed in all groups except those with cHIV/TB. Our findings support the need to screen for infections that could cause excessive liver damage prior to ATT or ART initiation, such as HBV.