Which continents lie partly in both the northern and southern hemispheres?

Northern

entirety of Europe

entirety of North America

entirety of Central America

the vast majority of Asia

more than half of Africa, just below the "horn".

Southern

Antarctica

Africa (approximately 33% )

Australia (the entire mainland is in the Southern Hemisphere, although the very northern part of Raja Ampat Islands in New Guinea are in the northern hemisphere)

South America (mostly, south of the Amazon River mouth in the east and Quito in the west)