Simultaneous source acquisition has become common over the past few decades for marine seismic surveys because of the increased efficiency of seismic acquisition by limiting the time, reducing the cost, and having less environmental impact than conventional single-source (or unblended) acquisition surveys. For simultaneous source acquisition, seismic sources at different locations are fired with time delays, and the recorded data are referred to as the blended data. The air-water interface (or free surface) creates strong multiples and ghost reflections for blended seismic data. The multiples and/or ghost reflections caused by a source in the blended data overlap with the primary reflections of another source, thus creating a strong interference between the primary and multiple events of different sources. We develop a convolutional neural network (CNN) method to attenuate free-surface multiples and remove ghost reflections simultaneously from the blended seismic data. The CNN-based solution that we develop operates on single traces and is not sensitive to the missing near-offset traces, missing traces, and irregular/sparse acquisition parameters (e.g., for ocean-bottom node acquisition and time-lapse monitoring studies). We illustrate the efficacy of our free-surface multiple attenuation and seismic deghosting method by presenting synthetic and field data applications. The numerical experiments demonstrate that our CNN-based approach for simultaneously attenuating free-surface multiples and removing ghost reflections can be applied to the blended data without the deblending step. Although the interference of primaries and multiples from different shots in the blended data makes free-surface multiple attenuation harder than the unblended data, we determine that our CNN-based method effectively attenuates free-surface multiples in the blended synthetic and field data even when the delay time for the blending is different in the training data than in the data to which the CNN is applied.