How Humanism (as the philosophical movement of the Renaissance historical period), the philosophy of the Enlightenment, and classical liberalism are related?
I have some difficulties distinguishing them from one another, since they share many of their (core) principles. (Humanism has later developed into so-called "secular humanism". I distinguish between Humanism and secular humanism principles in the following presentation).
Place and Time. The three emerged roughly around the same period of time and in the same place: roughly 16th-18th century Europe.
Freedom. They all insist on the freedom of the individual(1). Secular humanism will later, along with the philosophy of the Enlightenment and classical liberalism advocate for democracy.
Tolerance. They all advocate for tolerance.
Free market. The philosophy of Enlightenment, classical liberalism, and later secular humanism, advocate for some form of free market.
Reason and empirical sciences. Both Humanism and the philosophy of the Enlightenment defend the use of reason and empirical sciences over faith/mysticism/intuition/etc. At a very different degree, it can be argued that classical liberals also put emphasis on reason, to the extent that to them, a liberal society can function successfully only if individuals are responsible of themselves, which can be ensured by their fair use of reason (to identify what is in their own long term interest, e.g. not harming other unnecessarily and cooperating).
Progress. In the Humanism movement, it is more a moral progress. In the Enlightenment movement it is more a scientific and technical progress. The idea of progress does not stand as a principle in classical liberalism, but the materialistic progress that the application of classical liberalism main principles (free market and limited government) historically brought often serves as an argument for the adoption of classical liberalism.
So to me, Humanism, philosophy of the Enlightenment, and classical liberalism are in a continuity (and sometimes historically intertwined), with the liberty of the individual as a common thread. This continuity takes this shape:
Humanism 14th-17th century Europe (Petrarch, Montaigne, More) → Enlightenment 18th Europe (Locke, Smith, Voltaire) → classical liberalism 19th-20th Europe/U.S (Bastiat, Hayek, Friedman)*
The interesting point is they do are different movements, in the sense that they refined, modified each other according to the criterion concerning how to give greater freedom to the individual. Therefore, a classical liberal might not agree with a humanist, a humanist might not agree with an Enlightenment philosopher, etc.
But since it is the Humanism which introduced the emphasis on the freedom of the individual (more broadly designated as "the autonomy of the individual" [World History] [Britannica] at the time), one could hardly self-designates themselves as a classical liberal without recognizing their debt to the Humanism movement.
*It is worth noticing that these philosophical movements have been accompanied by the religious movement of the Reformation, the historical and geographical development of the latter maybe having definitive impact on how each philosophical movement were shaped according to their geographical position (Italy vs. France vs. Netherlands vs. Germany vs. Great Britain).
More in depth references
(1) Concerning Humanism and individualism
The period from the fourteenth century to the seventeenth worked in favor of the general emancipation of the individual. The city-states of northern Italy had come into contact with the diverse customs of the East, and gradually permitted expression in matters of taste and dress. The writings of Dante, and particularly the doctrines of Petrarch and humanists like Machiavelli, emphasized the virtues of intellectual freedom and individual expression. In the essays of Montaigne the individualistic view of life received perhaps the most persuasive and eloquent statement in the history of literature and philosophy.
Kreis, Steven (2008). "Renaissance Humanism". Retrieved 2009-03-03.