You can use the same method of interlocking shapes you used for the heart shapes. This tutorial shows you how to get started creating the familiar Olympic logo of interlocking rings.
1.)
Set the fill to none and the stroke to any color (I'm using a medium blue).
2.)
Select the ellipse 
tool and drag out a circle by holding the shift key as you drag.
3.) In the stroke palette, change the stroke weight to create a thicker outline.
4.) Go to Object > Path > Outline Path. This converts the outline to a object.
5.) With the selection tool, Alt drag to create a copy, then repeat 3 more times until you have 5 circles.
6.) Change the fill of each object to a different color (you can copy/paste the Olympic rings at the top of this page into your Illustrator file to use as a source of the colors you need -- just delete it before you turn in the file).
7.) Select top three top rings and from the align palette choose Vertical
Align Center 
and then horizontal Distribute center 
.
8.) With the three top objects still selected, go to the pathfinder palette
and choose divide 
.
9.) Choose Object > Ungroup
10.) Select the section where you want the rings to overlap and fill
the section to match the overlapping ring. Use the eyedropper 
tool to match the color.
Here's how:
Select the section, make sure fill is active on the color swatch, select the
eyedropper, then click the eyedropper on the color you want for the fill. You'll
need to do this for the middle ring and the right ring.
-----> 
11.) Use the Effects > Stylize > Inner Glow effect to give the rings a bit of a 3-D look.
12.) Now the rings appear to be overlapping, but you'll find that the rings are now chopped up into many sections. To join the rings together, select all the sections of each ring, then choose Object > Make compound path. When selecting the sections of each ring, you can do it very easily by selecting one section, then choosing Edit > Select > Same fill color. Then choose Object > Make compound path.
13.) Continue with the bottom rings until all of the rings appear to be interlocked.
14.) Finally, you may wish to select all the interlocking rings and group them.