Mixed marriage results

The Mahābhārata gives the answer for this in the Anuśāsanaparvan in the adhyāya on Varṇasaṅkara:

bhāryāścatasro viprasya dvayorātmāsya jāyate |
ānupūrvyāddvayorhīnau mātṛjātyau prasūyataḥ ||4||

The relevant part is the first half-verse, which essentially means as follows: Of the 4 wives a Vipra (a learned Vaidika Brāhmaṇa) can take (from the 4 Varṇas), the Vipra father is born as himself in the first two (Brāhmaṇa & Kṣatriya).