"1mg of substance equals 3IU. "
An IU has NO milligram, microgram, gram, etc. equality. An IU is an International Unit, which is a measurement of ACTIVITY, not true weight/mass. An IU is determined by an international commitee of scientists who wish to standardize biological compounds, such as vitamins (A, E, D, etc.), hormones (insulin, GH, etc.).
So in the case of GH, 1mg DOES equal 3IU's, but this is not the case for any other compound, such as beta-carotene, which is something like 6.25mg equals 1,000 IU's.
Also, IU's cannot be equated to a volume, since this is arbitrary. The IU's/ml is determined by the person who makes the solution.