This study aims to develop and evaluate a novel cardiovascular MR sequence, MyoFold, designed for the simultaneous quantifications of myocardial tissue composition and wall motion. MyoFold is designed as a 2D single breathing-holding sequence, integrating joint T1/T2 mapping and cine imaging. The sequence uses a 2-fold accelerated balanced SSFP (bSSFP) for data readout and incorporates electrocardiogram synchronization to align with the cardiac cycle. MyoFold initially acquires six single-shot inversion-recovery images, completed during the diastole of six successive heartbeats. T2 preparation (T2-prep) is applied to introduce T2 weightings for the last three images. Subsequently, over the following six heartbeats, segmented bSSFP is performed for the movie of the entire cardiac cycle, synchronized with an electrocardiogram. A neural network trained using numerical simulations of MyoFold is used for T1 and T2 calculations. MyoFold was validated through phantom and in vivo experiments, with comparisons made against MOLLI, SASHA, T2-prep bSSFP, and the conventional cine. In phantom studies, MyoFold exhibited a 10% overestimation in T1 measurements, whereas T2 measurements demonstrated high accuracy. In vivo experiments revealed that MyoFold T1 had comparable accuracy to SASHA and precision similar to MOLLI. MyoFold demonstrated good agreement with T2-prep bSSFP in myocardial T2 measurements. No significant differences were observed in the quantification of left-ventricle wall thickness and function between MyoFold and the conventional cine. MyoFold presents as a rapid, simple, and multitasking approach for quantitative cardiovascular MR examinations, offering simultaneous assessment of tissue composition and wall motion. The sequence's multitasking capabilities make it a promising tool for comprehensive cardiac evaluations in clinical settings.