The number of milligrams per millimole of a given substance is equivalent to that substance's molar mass. A millimole is one thousandth of a mole, and moles are a measure of the amount of substance, not mass. Therefore, the number of milligrams in a millimole varies depending on the substance being measured.
A mole is defined as the quantity of particles found in a sample of 12 grams of carbon-12. That number, 6.02 x 10^23, is called Avogadro's number. A substance's molar mass is the mass of one mole, or 6.02 x 10^23 atoms, of that substance. For an element, this number is displayed under its symbol on the periodic table. A millimole is one thousandth of that number, and it likewise contains one thousandth of a mole's mass.
For example, the molar mass of oxygen is 16 grams, and one millimole of oxygen contains 0.016 grams, or 16 milligrams; the number of milligrams per millimole is equivalent to the number of grams per mole. This holds true for all elements and compounds.