Written by Andre A. Pais:
Mipham seems to be one of the greatest inclusivists in the Buddhadharma. He always tries to embrace everything non-conflictingly, be it Pramana, Yogacara and Madhyamaka; Svatantrika and Prasangika; sutra and tantra; or inner and outer tantras (genral vajrayana and Dzogchen) [although I'm not so familiar here - nor anywhere else, for that matter...]. And usually Mipham uses a soft tone, despite not shying away from criticizing other views when need be.
As far as I understand it, from Mipham's introduction to Shantarakshita's Adornment of the Middle Way, his view is:
Mahayana, philosophically, is divided into Yogacara and Madhyamaka. Madhyamaka is further divided into Svatantrika and Prasangika.
Prasangika always keeps the 2 truths united, so they apparently have no interest in the conventional except for refuting it mercilessly, revealing its lack of nature. Even conventionally, phenomena are beyond the four conceptual extremes. [I don't know what this means conventionally].
Svatantrika splits the 2 truths:
The conventional can either be embraced as
1) according to the Sautrantika system, accepting external objects as being momentary and composed of partless particles - this is the view of Bhavaviveka. It's called Sautrantika-Svatantrika-Madhyamaka.
2) it can be accepted as according to the Cittamatra system that affirms that the objects of our experience are purely mental - this is the view of Shantarakshita. It's called Yogacara-Svatantrika-Madhyamaka.
It means that conventionally some Madhyamikas accept external objects, others see experience as mental. Any of these perspectives has its strength, and it's all for the sake of connecting with students who simply can't understand the sheer profundity of the prasangika stance beyond conceptual proliferation. Moreover, it allows Madhyamikas to debate non-buddhists or non-madhyamikas, since the former "seem" to accept objects in ways that are bridgeable to these other realist philosophical systems.
Concerning the ultimate truth, the characteristic of the Svatantrika approach is that it further divides the ultimate in two: the aproximate or concordant ultimate, and the actual ultimate. The aproximate or concordant ultimate is a conceptual "image" or conviction that is concordant with and aproximates the mind of the meditator to the actual ultimate. Again, this is all pedagogical, established so that practitioners can, step by step, approach the ultimate conceptually, ever more subtly, until all conceptually dissolves and the ultimate is directly perceived without the aid of anything extraneous to it - and thus the path of seeing is reached, first bhumi.
However, the final view of any Svatantrika is a middle way beyond extremes, indistinguishable from any prasangika.
This being said, Mipham defends Bhavaviveka (and praises Shantarakshita and his main treatise above anything else in the world!) while simultaneously subscribing to Chandrakirti's radical and uncompromising view. He resolves the issue, like already intuited, by saying that Svatantrika exists for the purpose of gradual-type of practitioners, while Prasangika aims at the sudden-type. He even compares the Prasangika approach with the Dzogchen view of self-liberation - everything is already instantaneously and spontaneously liberated; reality abides always and "intrinsically" as natural nirvana.
My only issue is that Mipham, and Shantarakshita, makes use of Cittamatra as the supreme explanation of merely the conventional, as a step towards Madhyamaka. The translators do note, however, that the Cittamatra that reifies the mind is the Cittamatra that was solidified by doxographers as a tenet system, and not the scriptural Cittamatra. It's this "tenet system Cittamatra" that is refuted by Madhyamaka, not necessarily the Yogacara tradition; and it is this type Cittamatra that is being used as an explanation of the conventional - and so, when approaching the ultimate, it needs to be abandoned in favor of the superior Madhyamaka view. Yogacara as it "actually" is, and not as it is portrayed by some madhyamikas, doesn't necessarily reify anything and consequently doesn't necessarily have to be abandoned in favor of Madhyamaka when reaching for the actual ultimate.
Concerning Tsongkhapa, as some authors and lineage masters have pointed out, he's a peculiar Madhyamika, because his apparently obsession with philosophical analysis has him constructing elaborate theories concerning the conventional, supported by his appreciation for the epistemological tradition. In this respect, he seems to come closer to Bhavaviveka than to his Madhyamaka hero, the glorious Chandrakirti.
On the other hand, contrary to other great Madhyamikas, namely Gorampa, the Karmapas and Mipham, Tsongkhapa does think that the ultimate is a non-affirming negation and that conceptuality can rise all the way to the actual ultimate. Therefore, the actual ultimate is actually a negation and thus not beyond the four ontological extremes. In this sense, by conceptualizing the ultimate, he again seems to come closer to the "aproximate ultimate" of the svatantrikas than to the actual ultimate beyond extremes of the prasangikas.