Early detection of Alzheimer's Dementia (AD) and Mild Cognitive Impairment (MCI) is critical for timely intervention, yet current diagnostic approaches remain resource-intensive and invasive. Speech, encompassing both acoustic and linguistic dimensions, offers a promising non-invasive biomarker for cognitive decline. In this study, we present a machine learning framework for the PROCESS Challenge, leveraging both audio embeddings and linguistic features derived from spontaneous speech recordings. Audio representations were extracted using Whisper embeddings from the Cookie Theft description task, while linguistic features-spanning pronoun usage, syntactic complexity, filler words, and clause structure-were obtained from transcriptions across Semantic Fluency, Phonemic Fluency, and Cookie Theft picture description. Classification models aimed to distinguish between Healthy Controls (HC), MCI, and AD participants, while regression models predicted Mini-Mental State Examination (MMSE) scores. Results demonstrated that voted ensemble models trained on concatenated linguistic features achieved the best classification performance (F1 = 0.497), while Whisper embedding-based ensemble regressors yielded the lowest MMSE prediction error (RMSE = 2.843). Comparative evaluation within the PROCESS Challenge placed our models among the top submissions in regression task, and mid-range for classification, highlighting the complementary strengths of linguistic and audio embeddings. These findings reinforce the potential of multimodal speech-based approaches for scalable, non-invasive cognitive assessment and underline the importance of integrating task-specific linguistic and acoustic markers in dementia detection.