Hello Stephen,
According to the moments of consciousness model yes, moments of breath are interspersed with moments of awareness, so discrete and so fast that they are imperceptible to most of us, but will be so in the later stages of meditation.
The term “continuous” means that there are more moments of awareness interspersed with attention, and those moments of awareness are such that you have an understanding of the quality and state of your mind while also holding attention on the meditation object. Continuous does not imply only one form of conscious experience – attention or awareness. Through the more expansive mental capacity achieved from meditating, by the end of stage 4, you can increase the moments of awareness with attention.
Regards,
Michael
Dharma Treasure teacher-in-training