<p>Human Immunodeficiency Virus (HIV) is a disease that attacks the human immune system, making individuals more vulnerable to opportunistic infections, including mpox. According to a report by the World Health Organization (WHO), over 50% of confirmed mpox cases also have HIV, particularly among men who have sex with men (MSM). In this study, we propose a compact mathematical model to describe the coinfection dynamics between mpox and HIV/AIDS, incorporating the impact of case detection and treatment for coinfected individuals. To reflect limited treatment capacity, we introduce a saturated treatment function, which reduces the maximum achievable treatment rate as the number of treated individuals increases. We perform a detailed mathematical analysis, including positivity of solutions, existence and stability of equilibrium points, and calculation of the basic reproduction number. We show that the basic reproduction number is determined by the maximum of two type-specific reproduction numbers, corresponding to the transmission of mpox or HIV/AIDS only. The disease can be eradicated from the population if this number remains below one. We identify two types of dominant endemic equilibrium and two types of coinfection endemic equilibrium, one of which corresponds to a scenario where mpox circulates only within the HIV-infected subpopulation. These results emphasize the importance of targeted interventions for both diseases, rather than focusing on only one. Using path-following techniques, we demonstrate that the model exhibits complex dynamics, including period-doubling bifurcations that lead to chaotic behavior. This chaotic regime results in unpredictable epidemic trajectories, which can significantly challenge intervention strategies. A codimension-2 bifurcation analysis highlights the intricate interplay between the coinfection transmission rate and the case detection rate, revealing multiple dynamical regimes such as stable coinfection endemic states, sustained oscillations, and chaotic outbreaks. Additionally, a global sensitivity analysis using the Partial Rank Correlation Coefficient (PRCC) method identifies the coinfection rate and the coinfection-induced death rate as key drivers of disease dynamics. We also find that increasing the coinfection rate not only amplifies the outbreak peak but also accelerates its emergence. These findings provide scientific insights to support the design of effective eradication strategies for both mpox and HIV/AIDS.</p>