The simple answer to the question of whether or not your child can wear aligners when they have a mixture of baby teeth and adult teeth is Yes. Context is key, here. There exists a very small window or time-frame where clear aligners are an acceptable option for young children. Usually, an orthodontist will simply wait until most if not all baby teeth are out and adult teeth have erupted before starting any type of aligner therapy. Aligners must be worn full-time to exert their influence (some exceptions do exist but these are rare). For children who are losing baby-teeth, the insertion and removal of aligners may prove uncomfortable when baby teeth are in the process of coming out (exfoliating). The natural process that occurs when baby teeth fall out involves an adult tooth erupting near to or directly underneath of the baby tooth it is meant to replace. This adult tooth eruption process will quite often result in a natural shortening of the baby tooth root which will cause the baby tooth to eventually get loose and fall out. As a baby tooth becomes more and more loose (mobile) it tends to be more sensitive to manipulation. At this point the insertion and removal of aligners will probably be considered an irritation to most children and this is not a good time to consider aligner therapy.
Having said that, a window of time exists wherein most baby teeth are solid and some adult teeth are fully-erupted and present for positioning. In this window (typically somewhere from 8-10.5 years old) a young patient could conceivably pursue aligner treatment. As dental development is somewhat variable this window will vary from patient to patient. The obvious requirement, here, is that the patient is able to comply with full-time aligner wear and that their baby-teeth are solid enough to not cause irritation during aligner insertion and removal. If these conditions are met, aligner therapy may be a treatment option for young orthodontic patients.
Following any early treatment for a young orthodontic patient, a period of observation during growth and development will occur. Once all the adult teeth are erupted a second evaluation would consider further treatment is warranted (ideally it would not be) and another set of aligners would be designed and used to continue the work accomplished at the younger age.