Obstructive sleep apnea (OSA) is a common sleep disorder characterized by recurring breathing pauses during sleep caused by a blockage of the upper airway (UA). OSA is generally diagnosed through a costly procedure requiring an overnight stay of the patient at the hospital. This has led to proposing less costly procedures based on the analysis of patients' facial images and voice recordings to help in OSA detection and severity assessment. In this paper we investigate the use of both image and speech processing to estimate the apnea-hypopnea index, AHI (which describes the severity of the condition), over a population of 285 male Spanish subjects suspected to suffer from OSA and referred to a Sleep Disorders Unit. Photographs and voice recordings were collected in a supervised but not highly controlled way trying to test a scenario close to an OSA assessment application running on a mobile device (i.e., smartphones or tablets). Spectral information in speech utterances is modeled by a state-of-the-art low-dimensional acoustic representation, called i-vector. A set of local craniofacial features related to OSA are extracted from images after detecting facial landmarks using Active Appearance Models (AAMs). Support vector regression (SVR) is applied on facial features and i-vectors to estimate the AHI.