As a WHM, most of the time in casual content you will be the main healer. If you're partnered with a SCH or AST, they will usually be shielding the party, buffing (AST cards), and helping out with emergency heals (lustrate, essential dignity), raises, etc. If you don't have a raise macro, you may wish to consider it, so they can see whether you've raised someone right away and that will let them know you've already done it.

If you're doing cutting edge progression content such as Extreme fights, you'll want to take a second with the other healer to establish who heals what tank, or how long you're expected to solo heal. For instance if I DF Ravana as SCH, I ask how long the other healer can solo heal. if I DF Ravana as WHM, I expect to solo heal for most of the fight. If I were healing Thordan, the WHM generally solo heals until the two knights phase, then they choose a tank and keep up Medica II and do party heals.

SCH heals pair extremely well with WAR, so if your party composition is DRK/PLD and WAR, and yourself and a SCH, it will be generally expected that the SCH will heal for WAR and you'll heal for the other tank.