If what is meant by infiniteness is that it is not limited by any boundaries, even the boundary of 'createdness' or 'being created' and 'reliance' and 'need', then it must be said that nothing other than Allah has surpassed such boundaries, and from this perspective, there is no difference between the Ahlul-Bayt and other people. Therefore, there is nothing other than Allah that is beyond ALL boundaries.
This means that even the greatest signs of Allah in the universe (i.e., the infallibles), are limited by being His servants, and if they have reached the pinnacles of perfection and beauty, it is because of them being complete servants of God. The more the submission and need (expressing one's need before Allah), the more one's existential scope will expand, despite being dependant and reliant totally on God; it is because of this that it has been said: "Ubudiyyat (being a servant) is something whose core is Rububiyyah (Lordship)."; meaning that it is through total submission and servitude that one becomes the vicegerent of God and attains existential encompassment of everything other than God.
However, if what you mean is that their qualities are beyond our imaginations and comprehension, then one must say that since these qualities of the Ahlul-Bayt originate from divine manifestation, their limits are unknown and incomprehensible to us, as Imam Ali (as) says: "[Just] don't say we are deities, [then you can] say anything about our virtues that you desire, because you will never be able to reach the core of what Allah has endowed us with."
 "قال الصادق ع العبودیة جوهر کنهها الربوبیة", Imam Sadiq (AS), Misbah al-Shari'ah, p. 7, Al-A'lami Lil-Matbu'at Institute, 1400 AH.
 "أَنَا عَبْدُ اللَّهِ عَزَّ وَ جَلَّ وَ خَلِیفَتُهُ عَلَى عِبَادِهِ لَا تَجْعَلُونَا أَرْبَاباً وَ قُولُوا فِی فَضْلِنَا مَا شِئْتُمْ فَإِنَّکُمْ لَا تَبْلُغُونَ کُنْهَ مَا فِینَا وَ لَا نِهَایَتَهُ فَإِنَّ اللَّهَ عَزَّ وَ جَلَّ قَدْ أَعْطَانَا أَکْبَرَ وَ أَعْظَمَ مِمَّا یَصِفُهُ وَ أَصِفُکُمْ أَوْ یَخْطُرُ عَلَى قَلْبِ أَحَدِکُم", Majlisi, Muhammad Baqir, Bihar al-Anwar, vol. 26, p. 1, Al-Wafa' Institute, Beirut, 1404 AH.