A standard midpoint composite begins with two accurately calculated natal charts. For each planet or point, the calculator measures the shortest distance between the two natal positions and places the composite point halfway between them.
Imagine one person has the Sun at 10 degrees of Aries and the other has the Sun at 10 degrees of Gemini. The shortest arc between those positions is 60 degrees, so the midpoint falls at 10 degrees of Taurus. That becomes the composite Sun. Real calculations must also handle positions that cross the beginning and end of the zodiac correctly.
The completed chart contains composite planetary positions, aspects, and, when the birth data supports them, angles and houses. These positions are calculated values. They do not describe one moment when the planets actually occupied that arrangement in the sky.