Engage your abdominal muscles. Pull your navel toward your spine and feel a closing-in of the ribcage. Maintain a strong, tight core throughout your preparation, jump and landing.
Bend your knees into a nice deep demi-plié as preparation for your jump. Avoid being a dead-weight in your partner's hands, as his task is to support -- not provide power for -- your jump. Instead, rely on your own leg muscles and core strength to power the jump. Return to a soft deep demi-plié when you land; doing so will cushion your landing and keep it quiet.
Avoid "sitting" at the bottom of your plié; doing so will hinder your jump. When you reach the extreme point of the downward motion of the plié, immediately drive yourself upward.
Articulate through your feet as you push off and as you land. Use the strength and flexibility you have acquired in your ankles and feet to propel you upward and to soften your landing.
Hold your back upright throughout your jump. Avoid leaning forward from the waist or your partner will have more difficulty controlling you when you push off from the floor and as you land.
Trust your partner. Allow him to guide the direction of your jump and to contribute to its height. Give into the gentle pressure he exerts as he lifts you upward. Communicate openly with him if you feel there are timing or other issues that are hindering your jumps.