I have not read the ASIC Handbook but I know about the Aplication Specific Integrated Circuits book. This book is a bible for ASIC design. It has every step from coding to floorplanning. It's an engineering book and you can use it as a reference.
Maybe as a beginner it will be difficult to read it from beginning to the end but the chapters are divided in such way that they are complete by themselves and you can study whatever part you want.
What you have studied so far is good, you can also see about synthesis and simulation in this book.
Most things you will see and understand when you will start working.
You can find the Aplication Specific Integrated Circuits book in the EDA forum in this link:
and many other books about ASIC if you search there.