It sounds like you are describing a stratovolcano, also known as a composite volcano. Stratovolcanoes are characterized by their layered structure, consisting of alternating deposits of lava flows, ash, and volcanic rock. They typically have a steeper profile compared to other types of volcanoes, particularly at their summits, but they generally feature more gently sloping sides leading down from the summit.
Stratovolcanoes are known for their explosive eruptions, which can produce pyroclastic flows, as well as effusive eruptions that create lava flows. Notable examples of stratovolcanoes include Mount St. Helens in the United States, Mount Fuji in Japan, and Mount Vesuvius in Italy.