You will have to set up a series of custom bullet styles, using, in addition, the "Style for following paragraph" option found in the Style creation/modification dialogue.

One way is to create the bullet styles you want, basing each on "No Style," rather than Normal, and giving them a custom name; or, if you don't need Word's default bullets, simply modify these in the default numbering schema. (This was made more obscure and more complicated to do in 2007; I will ask you to look it up, rather than running through it all here.)

After creating all the bullet styles, start with the first level, go into the style modification dialogue, and set the second style as the "Style for following paragraph" option.