Please note that this is not a "recipe" or a constructional article.  It is the basis of a project methodology upon which you can build to create an object of your own choosing..  Amend the method as you see fit but take care when using tools: don't start a project like this, and don't use any power tools unless you are competent to do so and/or are being supervised by a trained operator.  No dimensions are given so that you can vary things to meet your needs.

The notes assume that you have access to a bandsaw (but you could use a handsaw) and a scrollsaw/fretsaw (but you could use a coping saw).

If you plan to split the box to create two boxes that will meet and kiss in the middle, then this split line needs to be planned now too.  If you do this, the compartments will be yet smaller - so work out your scheme on a piece of paper beforehand.  (This is also the best way to get a decent heart shape - full and plump - and from it draw a pattern you can trace.  A photocopier can be useful to adjust your pattern size.)

Having sawn your block into three, you now get to stick it back together using double-sided tape and ensuring that you get the pieces in exactly the same orientation as when you started.  (Keep the grain pattern matched exactly.)

Whilst this dries, you can be carefully cleaning up the inside faces of the box apertures.  The finish is less critical if the box is going to be lined when complete.  If leaving a natural wood finish, extra care and patience will be needed at this stage.

5)  The body(ies) can now be carefully aligned with the base(s) and glued in place.

6) Finally, finish the outside of the box, holding all pieces in perfect alignment (more double sided tape between lid and body may help.)  If it is wished to sculpt the lid(s) to give a 3D form, now is the time to do it.  Once everything is shaped to your satisfaction, finally sanded and treated with the required finish, staining etc., you can dress the inside by applying self-adhesive felt or spray-on flock, unless you have chosen a natural finish.  A final coat of wax and you should have a family heirloom.

FOOTNOTES:  A similar method can be use to create the box using a router instead of a scrollsaw to hollow out the interior.  In this case, do not cut off a slice for the base of the piece but leave the base and body as a single block.  Instead of sawing out the waste from the interior, make a pattern so that you can use a router with a guide bush, or a bearing-guided profile cutter to hollow out the interior to the desired depth.  To locate the lid on the body, you will need to hand-make inserts for the lids (see para. 4, above) since the waste pieces used in the sawn version will have been reduced to shavings by the router method!